The 26-year-old was born in Germany but has played 18 times, scoring five goals, for the Turkish national side.
Tosun scored 24 goals last season as he helped Besiktas to the Super Lig title and has one goal in three appearances so far this season.
Crystal Palace are yet to find the back of the net in their opening three Premier League games, losing to Huddersfield, Liverpool and Swansea.
Meanwhile, Newcastle are willing to let striker Dwight Gayle leave the club as long as they can find a suitable replacement.